Question

A small body of super dense material, with mass equal to half of that of earth but whose size is very small compared to that of earth, starts from rest at the height h<<R above the earths surface. It reaches the earths surface in time given by

• A. $\sqrt{\frac{2h}{g}}$
• B. $\sqrt{\frac{4h}{3g}}$
• C. $\sqrt{\frac{2h}{3g}}$
• D. $\sqrt{\frac{h}{g}}$

Answer 1

Answer: (B)

$\sqrt{\frac{4h}{3g}}$

As the masses are comparable, both the earth and the body will move upto their centre of mass:
$\frac{M}{2}\left(x\right)=M(h-x)=x=\frac{2h}{3}$
Time taken, $t=\sqrt{\frac{2x}{g}}=\sqrt{\frac{2\left(\frac{2h}{3}\right)}{g}}=\sqrt{\frac{4h}{3g}}$